The purpose of this paper is to investigate the main controlling factors of shale gas production in the context where well-induced fractures, extending from the well perforations, improve reservoir conductivity and performance. A mathematical 1D+1D model is presented which involves a high-permeable fracture extending from a well perforation, through symmetrically surrounding shale matrix with low permeability. Gas in the matrix occurs in the form of adsorbed material attached to kerogen (modeled by a Langmuir isotherm) and as free gas in the nano-pores. The pressure gradient towards the fracture and well perforation causes the free gas to flow. With pressure depletion, gas desorbs out of the kerogen into the pore space and then flows to the fracture. When the pressure has stabilized, desorption and production stop.
The production of shale gas and mass distributions indicate the efficiency of species transfer between fracture and matrix. It is shown that the behavior can be scaled and described according to the magnitude of two characteristic dimensionless numbers: the ratio of diffusion time scales in shale and fracture α, and the pore volume ratio between the shale and fracture domains β. Properties of fracture and matrix are varied systematically to understand the role of the fracture matrix interaction during production. Further, the role of fracture geometry (varying width) is investigated. Input parameters from experimental and field data in the literature are applied.
The product αβ expresses how much time it takes to diffuse the gas in place through the fracture to the well compared to the time it takes to diffuse that gas from the matrix to the fracture. For αβ ≪ 1 the residence time in the fracture is of negligible importance and fracture properties such as shape, width and permeability can be ignored. However, if αβ ≈ 1 the residence time in the fracture becomes important and variations in all those properties have significant effects on the solution.
The model allows intuitive interpretation of the complex shale gas production system. Furthermore, the current model creates a base which can easily incorporate non-linear flow mechanisms and geo-mechanical effects that are not readily found in standard commercial software, and further be extended to field scale application.